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More or Less back for more

Plus's favourite radio show on all things mathematical is back on the air. More or Less has two series a year on BBC Radio 4, exploring maths in politics, health, avalanches, and much more. In the first shows of this season they have already covered drug testing in sport, the economics of climate change, uncovered the
games behind hospital waiting times, and the perverse nature of randomness.

The show is produced in association with the Open University, which provides additional material on their site. You can hear all the past shows online at the More or Less site, and listen live every Monday at 4.30pm on BBC Radio 4.

You can read more about More or Less from presenter Andrew Dilnot in a past article on Plus.

The famous mathematical family, the Bernoullis, produced an astounding eight mathematicians over three generations. The sheer number of them, and the family habit of using the same first names, required the numbering system you see above to keep track of them all. And given the family's mathematical success, you would think that each generation was actively encouraged to study the subject. But
instead the mathematical members of the family often had to study mathematics and astronomy against the wishes of their parents. Indeed there were enough quarrels, backstabbing and even untimely deaths among the Bernoullis to script a soap opera.

Jacob (I) Bernoulli was the first member of the family to study maths, and taught his brother Johann (I) who had been forced to study medicine. The brothers worked on similar topics, such as calculus (Jacob was the first mathematician to use the term 'integral') and studying families of curves such as the catenary, the curve of a suspended string. However, in what would prove to be typical
behaviour in the family, the brothers soon went from collaborators to rivals, publicly criticising each other's intellect and competing to solve the same mathematical problems.

Jacob and Johann taught their nephew, Nikolaus I, mathematics, and Nikolaus assisted his uncle, Jacob, in publishing his works. Nikolaus is known for posing the probability problem the "St Petersburg paradox", which describes a gambling game that no-one would reasonably play, despite a possibly infinite prize.

Nikolaus's cousin Daniel (son of Johann) provided an explanation of the St Petersburg paradox. Daniel, probably the most famous mathematician of the family, did his most important work on fluid dynamics, and gave the Bernoulli principle. However, continuing the family's bitter history, Daniel had a difficult relationship with his father Johann, who did not want him as a mathematical
competitor. Johann tried to stop Daniel from studying mathematics, and even attempted to plagiarise Daniel's greatest work, "Hydrodynamica".

Johann I's other two sons were also mathematicians. His favourite Nikolaus II worked on the problem of trajectories, and the mathematical arguments behind Newton and Leibniz's dispute over who had invented calculus. Johann II worked in mathematical physics.

Johann II also had two mathematical sons. Johann III was a child prodigy, and was just 19 years old when he was appointed to the Berlin Academy. He produced work in astronomy and probability, but his accounts of his travels in Germany had a greater impact historically. Jacob II worked on mathematical physics at the St Petersburg Academy of Sciences, and married Euler's granddaughter. Sadly he
drowned in the Neva River when he was only 29 years old.

The Bernoulli family, despite its infighting and bitterness, dominated mathematics in the 17th and 18th centuries. Together with their contemporaries Newton, Leibniz, Euler and Lagrange, they laid many of the foundations of mathematics and physics that we still use today.

"There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician." - Daniel Bernoulli

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Plus new writers award - the entries are in!

Our inaugural writing competition has just closed, and we were very pleased to arrive to overflowing mailboxes — both virtual and real!

Our esteemed panel of judges: best selling authors Marcus du Sautoy and John Barrow, and Economist correspondent and ex-editor of Plus Helen Joyce, will be judging the excellent entries over the next couple of months. The prize pool has swelled over the year and now includes many of the best popular science books, as well as a subscription to nature and an iPod!

So stay tuned for the December issue of Plus when you can find out who won and how they brought mathematics to life!

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Celebrating mathematics at work

The relevance and usefulness of mathematics is most clearly demonstrated in its application to real-world problems, many of which have featured in Plus over the years. To celebrate mathematics at work in the real-world, the International Council for Industrial and Applied Mathematics have announced the winners of the five ICIAM prizes
for 2007.

The Pioneer Prize, recognising innovations in applied mathematics, was jointly won by Ingrid Daubechies (Princeton University, USA) and Heinz Engl (Johannes Kepler Universität Linz, Austria). Daubechies' work on wavelets has found widespread use
in image processing and frequency analysis. Engl was recognised for his work on inverse problems to the solution of a wide range of industrial problems and for his promotion world-wide of industrial and applied mathematics.

The Collatz Prize is awarded to outstanding applied mathematicians under the age of 42. It was won by Felix Otto (Universität Bonn, Germany) for his fundamental contributions in areas ranging from micromagnetics to mass transportation problems.

Joseph Keller (Stanford University, USA) won the Lagrange Prize for his exceptional contributions to the field. Not only has he influenced the course of modern applied mathematics over the last 50 years, he has also had a great impact in pure mathematics as well. He developed the Geometrical Theory of Diffractions that provided the first
systematic description of wave propagation around edges and corners of an obstacle. It has been widely used for radar reflection from targets, elastic wave scattering from defects in solids, acoustic wave propagation in the ocean radar and many other fields. He has also made contributions to quantum mechanics, optics, acoustics, biophysics and biomechanics and transport theory.

Peter Deuflhard (ZIB Berlin, Germany), winner of the Maxwell Prize, is one of the founders of modern scientific computing, and is described as having made a contribution to applied mathematics that is without parallel, including applications in chemical engineering, medicine and biotechnology, microwave technology and nano-optics.

The Su Buchin Prize is more unusual in the field of mathematics, recognising the "application of Mathematics to emerging economies and human development". The winner, Gilbert Strang (MIT, USA), is one of the most recognised mathematicians in the developing world through his promotion of mathematical research and education across the globe. As well as
numerous visits himself, he has organised visits by other mathematicians to developing countries, and his educational materials are available on the web, free-of-charge to any user anywhere in the world, through MIT's OpenCourseWare. Alongside his contributions in bringing mathematics to people around the world, his research has made contributions in
many areas of pure and applied mathematics.

The prizes will be presented at the International Congress for Industrial and Applied Mathematics in Zürich next year, a major international celebration of mathematics in action. More information on the prizes, and the winners, can be found at the ICIAM website. And you can read more about industrial mathematics on Plus.

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Einstein passes with 99.5% result

On September 14th, after 3 years observing a rare double pulsar, an international team led by Prof. Michael Kramer from the Jodrell Bank Observatory announced staggering results confirming Einstein's general theory of relativity to 99.5% accuracy. The observations were made on a pair of pulsars orbiting each other approximately 2000 light years
from Earth. Each pulsar weighs a little more than the Sun but has a diameter of around 10km. The extreme mass of the pair gives us a rare opportunity to study the predicted effects of general relativity.

Sometimes when a large star collapses it becomes a very small, very dense object known as a neutron star. A pulsar is a rotating neutron star. Pulsars are extremely useful for astronomical observations as they emit constant, powerful beams of radio waves similar to how a lighthouse emits a beam of light. Each time a beam sweeps past Earth we observe a distinctive radio pulse. By precisely
measuring the time between pulses we can make detailed calculations on the effect gravity is having on the radio waves. By current theory, this behaviour should be governed by the laws of general relativity and it turns out that the predictions match with observation to an astonishing level of accuracy.

Another very important result is that the distance between the two pulsars is shrinking by around 7mm per day. This also agrees with Einstein's predictions. According to general relativity, the pulsars should be emitting gravitational waves and although these waves have never been directly detected, their emission should cause the pulsar system to lose energy. The observable effect of this
would be the pulsars spiraling towards each other by precisely the amount observed giving compelling evidence for the existence of gravitational waves.

However Dr. Kramer believes that there are still many more exciting results to come: "The double pulsar is really quite an amazing system. It not only tells us a lot about general relativity, but it is a superb probe of the extreme physics of super-dense matter and strong magnetic fields but is also helping us to understand the complex mechanisms that generate the pulsar's radio beacons." He
concludes; "We have only just begun to exploit its potential!"

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School maths to beat climate change

Good maths and science school education is vital in dealing with climate change according to Frances Cairncross, President of the British Asoociation of the Advancement of Science and Chair of Britain's Economic and Social Research Council. Speaking at the BA Festival of Science
taking place in Norwich last week, Ms Cairncross said that trying to mitigate the impact of climate change is no longer sufficient: we need to put equal effort into preparing for a world with a different climate. "We need to think now about policies that prepare for a hotter, drier world, especially in poorer countries. That may involve, for instance, developing new crops, constructing flood
defences, setting different building regulations, or banning building close to sea level."

To develop such strategies we don't only need scientists, but also a well-informed public that can partake in public debate and help to drive change. A good school education in maths and science is vital in creating both. "An innumerate population is less likely to devise good solutions to climate change and a host of other environmental problems than one at home with mathematical and
scientific concepts," Ms Cairncross said. "Perhaps we need to experiment with a bounty for every A grade maths A-level taken in a maintained school... or a couple of extra UCAS points for each A grade."

Climate change features strongly at this year's Science Festival and the scientists' predictions are dire, giving us only a few years to seriously curb our carbon emissions or face drastic change. Ms Cairncross called the Kyoto agreement to cut greenhouse gas emissions "ineffectual" and suggested that an effective strategy to deal with environmental problems involves "persuading this
generation to accept sacrifices on behalf of posterity." Such altruistic behaviour is only likely to come about if people understand the risks and realities involved in climate change and for this they need a sound mathematical and scientific grounding.